Bottom Line:
It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity.However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants.Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses.

ABSTRACTThe modulation of the sensitivity, or gain, of neural responses to input is an important component of neural computation. It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity. This gain control scheme was developed and explored with static inputs, where the membrane and spike train statistics were stationary in time. However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants. Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses. Moreover, the degree of divisive scaling of the dynamic response is quantitatively the same as the steady-state responses--thus, gain modulation via balanced conductance fluctuations generalizes in a straight-forward way to a dynamic setting.

pcbi-1000365-g001: Input-output schematic for population of LIF neurons with a combination of driving input and balanced background fluctuations.(A) Excitatory driving input with rate . (B) Balanced fluctuating background inputs with rates . For illustrative purposes the evolution of is shown when ; three intensities of background input are shown. (C) Sample realization of the LIF dynamic. (D) Raster plots of the output spikes are shown (Monte Carlo). (E) The output firing rate , computed by the population density method (see Equations (6)–(8)), is a fast and efficient method for capturing the output firing rate. It matches the average firing rate of 100,000 random LIF neurons computed by Monte Carlo simulation.

Mentions:
Figure 1 is a schematic diagram of the representative leaky integrate-and-fire neuron from the population receiving the combination of driver and balanced inputs. For the sake of exposition, we focus on three different intensities of balanced background inputs: to be 1100 s−1, 1400 s−1, and 1900 s−1 (with corresponding , 1361.24 s−1, and 1847.40 s−1, respectively), which we respectively label low (black), medium (red), and high (blue). Chance et al. [11] modified the background level by various rate factors and labeled the regimes 1X, 2X, etc., which is slightly different than our convention of low, medium, and high. However, the resulting steady-state input/output curves (Fig. 2) are similar to those in Chance et al. [11]. Also, our results below hold equally well for many other sets of balanced background activity. For a particular background intensity (low in this case) with random excitatory drive , the output is random (see spike raster plots). As the balanced background activity is increased, the variability in the voltage also increases (Fig. 1B).

pcbi-1000365-g001: Input-output schematic for population of LIF neurons with a combination of driving input and balanced background fluctuations.(A) Excitatory driving input with rate . (B) Balanced fluctuating background inputs with rates . For illustrative purposes the evolution of is shown when ; three intensities of background input are shown. (C) Sample realization of the LIF dynamic. (D) Raster plots of the output spikes are shown (Monte Carlo). (E) The output firing rate , computed by the population density method (see Equations (6)–(8)), is a fast and efficient method for capturing the output firing rate. It matches the average firing rate of 100,000 random LIF neurons computed by Monte Carlo simulation.

Mentions:
Figure 1 is a schematic diagram of the representative leaky integrate-and-fire neuron from the population receiving the combination of driver and balanced inputs. For the sake of exposition, we focus on three different intensities of balanced background inputs: to be 1100 s−1, 1400 s−1, and 1900 s−1 (with corresponding , 1361.24 s−1, and 1847.40 s−1, respectively), which we respectively label low (black), medium (red), and high (blue). Chance et al. [11] modified the background level by various rate factors and labeled the regimes 1X, 2X, etc., which is slightly different than our convention of low, medium, and high. However, the resulting steady-state input/output curves (Fig. 2) are similar to those in Chance et al. [11]. Also, our results below hold equally well for many other sets of balanced background activity. For a particular background intensity (low in this case) with random excitatory drive , the output is random (see spike raster plots). As the balanced background activity is increased, the variability in the voltage also increases (Fig. 1B).

Bottom Line:
It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity.However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants.Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses.

ABSTRACTThe modulation of the sensitivity, or gain, of neural responses to input is an important component of neural computation. It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity. This gain control scheme was developed and explored with static inputs, where the membrane and spike train statistics were stationary in time. However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants. Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses. Moreover, the degree of divisive scaling of the dynamic response is quantitatively the same as the steady-state responses--thus, gain modulation via balanced conductance fluctuations generalizes in a straight-forward way to a dynamic setting.